Design sensitivity analysis of non‐linear structural systems part I: Theory

Abstract

SUMMARYA unified approach is presented for design sensitivity analysis of non-linear structural systems that include truss, beam, plane elastic solid and plate components. Both geometric and material non-linearities are treated. Sizing design variables, such as thickness and cross-sectional areas of components of individual members and built-up structures, are considered. A distributed parameter structural design sensitivity analysis approach is used that retains the continuum elasticity formulation throughout the derivation of design sensitivity analysis results. Using this approach and an adjoint variable method, expressions for design sensitivity in terms of design variations are derived in the continuous setting which can be evaluated numerically using analysis results of finite element analysis. Both total Lagrangian and updated Lagrangian formulations in non-linear analysis of solid mechanics are used for design sensitivity analysis. Numerical implementation of design sensitivity analysis results using existing finite element code will be presented in Part I1 of this paper.

Multiphase Topology Optimization Considering Elastoplastic Cyclic Deformation and Accuracy Validation of Analytical Sensitivity

“…2) Schwarz and Ramm 3) Maute et al 4) , Schwarz et al 5) Choi and Santos 6) Ohsaki and Arora 7) A2 , Vol. 70, No.…”

Finite element response sensitivity analysis: a comparison between force-based and displacement-based frame element models

“…We assume without loss of generality that the time continuous -spatially discrete equation of motion (1) is integrated numerically in time using the well-known Newmark-β time-stepping method of structural dynamics [3], yielding the following nonlinear matrix algebraic equation in the unknowns u n+1 = u(t n+1 ): (2) where (3) and are parameters controlling the accuracy and stability of the numerical integration algorithm and is the time increment. Equation (2) represents the set of nonlinear algebraic equations for the unknown response quantities that has to be solved at each time step .…”

“…Significant research has been devoted to the general problem of design sensitivity analysis (see [1,2,16,17]). Consistent finite element response sensitivity analysis methods are already well established for displacement-based finite elements (see [4,6,10,18]).…”

Shape sensitivity analysis for structural problems with non-linear material behaviour

“…If this is the case, the structural sensitivity analysis must be computed using an incremental approach. Typically, this is done using expression (1), where the sensitivities of the displacements are obtained as an addition of increments. In this work, the approach proposed by Kleiber et al [10,13,14] has been used.…”